Parallel Structural Optimization Applied to Bone Remodeling on Distributed Memory Machines

摘要

This paper demonstrates parallel structural optimization methods on distributed memory MIMD machines. We have restricted ourselves to the simpler case of minimizing a multivariate non-linear function subject to bounds on the independent variables, when the objective function is expensive to evaluate as compared to the linear algebra portion of the optimization. This is the case in structural applications, when a large three-dimensional finite element mesh is used to model the structure. This paper demonstrates how parallelism can be exploited during the function and gradient computation as well as the optimization iterations. For the finite element analysis, a 'torus-wrapped' skyline solver is used. The reflective Newton method which attempts to reduce the number of iterations at the expense of more linear algebra per iteration is compared with the more conventional active set method. All code is developed for an Intel iPSC/860, but it can be ported to other distributed memory machines. The methods developed are applied to problems in bone remodeling. In the area of biomechanics, optimization models can be used to predict changes in the distribution of material properties in bone due to the presence of an artificial implant. The model we have used minimizes a linear combination of the mass and strain energy in the entire domain subject to bounds on the densities in each finite element. Early results show that the early reflective Newton method can outperform active set methods when a significant number of variables are not active at the minimum.